Self-Taught vs. Academic: The Need for Formal Education in Mathematics

[twofish-quant]

Lecturing to 200 students has recently become obsolete, thanks to video technology (as of maybe the 1930s or earlier, if anyone was paying attention, and much more so with the internet). Why are we still doing these silly things?

I don't think it is obsolete. Video technology can substitute some of the functions of the lecture, but there are still a lot of missing functionality, and if you look carefully at *why* people still have 200 person in-class lectures you can see what some of those functions are.

Off the top of my head:

1) Synchronicity. If you have 200 people going to the same lecture and reading the same page on the same book, then you know who to talk to if you have a problem on that page. Suppose you listen to a lecture on open courseware. You don't understand something. Now what?

2) Feedback. There is a lot of social feedback that happens in a lecture. A professor can look at the class, count the number of students, see how many people are asleep, and then adjust the pace of the course. Also have all of the students in the same room is useful because the students can look at each other, find other students that are in the same class, create social networks, and then complain about the teacher. If you are in a 200 person lecture class, and you are the only one that has difficulty understanding the teacher you are in a completely different situation than if you have 150 people muttering about how incompetent the teacher is.

3) Evaluation. If you have everyone in the same room, give the same test, and then look at the scores, it's much easier to figure out what is going on. If you have people taking the same test at different times, then people that take the test later are going to be able to see the earlier answers. If you give different tests, then you are looking at a hellish problem trying to normalize the scores.

4) Group motivation. Just being part of a group is psychologically motivating.

Now all of these things can be worked around (UoP has some interesting solutions to the synchronicity problem), but it's not the case that you can record some videos and declare victory. It's a very tricky problem.

 

[twofish-quant]

There's also institutional inertia. One thing about universities is that internal funding is based on credit hours, and there are "chains of responsibility" that are based on who is the instructor of record in the catalogue. Credit hours and required courses are also the "currency" for bureaucratic turf wars.

Now if you move away from self-contained classes, then this doesn't work anymore. So you have to come up with some new language to distribute money and power. Now you can throw your hands up and refuse to play these bureaucratic games, but if you don't come up with a new system to distribute money and power, then people won't get paid, and things won't get done.

It's really tempting to say this is useless. You can just go to the library, log onto the computer network, take a course, and not have to worry about any of this nonsense. The problem is that the library, the computer network, the dormitory, the janitors, and everyone else is getting paid through the current system (i.e. what typically happens is that the university puts a 40% tax on grants and education expenses to pay for these services) so if you wipe out the system for paying for all of this, then the network and the libraries go dark.

 

[dijkarte]

I still cannot comprehend the idea that stuffed classes with many students going to help the teaching/learning process. It's two-way process, teaching-learning, teacher-learner(s).
The signals that carry information from the teacher to the students will be subject to a lot of disturbance and noise. The more students the weaker the teaching signal energy is. And based on my experience this weak information signal can trigger the "I want to sleep" part of the brain which is why you find many students either are sleeping or skipping classes.
:D

 

[jtbell]

3) Evaluation. If you have everyone in the same room, give the same test, and then look at the scores, it's much easier to figure out what is going on. If you have people taking the same test at different times, then people that take the test later are going to be able to see the earlier answers. If you give different tests, then you are looking at a hellish problem trying to normalize the scores.

If you don't have everybody taking the test at the same time in the same room, you also have the little problem of ensuring that Joe Schmoe, who is registered for the course, is actually taking the test, and not paying Suzy Smart to take it for him.

Of course, this is in principle separate from the issue of group lectures. I understand that in Europe, grades in many or most courses are determined by the final exam at the end of the course, so students actually have to meet all together only once, anyway. They can attend or not attend lectures, tutoring sessions, etc. as they please, and they're responsible for the final outcome. In the U.S., I suspect that most students would not take very well to this system, at least initially. They're used to lots of hand-holding, with frequent benchmarks along the way in the form of homework grades, quizzes and midterm exams, all of which get included in the final grade.

 

[CDTOE]

@twofish-quant

I agree with you that it's wrong to evaluate a person's understanding and skills on a subject according to his grades, but what can you do if some teachers, a lot with PhD, think that this is the best strategy to evaluate a student? for this reason, I have rarely interacted with students who have ambition to learn for the purpose of getting new knowledge and skills, because most of students I interacted with, even those with high grades, pursue good grades and that's their most ambitious goal; how to get an A on that course?

This semester I have a complex analysis course for electrical and mechanical engineering students, taught by a professor in a pure mathematics way. Although the professor is very well-experienced and knowledgeable on different subjects, and he always pushes students to learn and to read, they get a book containing old major and final exams and they study from it only, because the new tests are very similar to the old ones. They never think about getting to understand the subject of complex analysis in a formal way. They just want to to solve old exams and get a good grade on their new exams. In the first class, the professor put a binomial raised to the third power, and students, although a lot of them have top A grades, couldn't expand the term!

That's one of the reasons I'm opposed to the way university teaches students, because most professors push students to care more about grades rather than real understanding of subjects and developing actual engineering skills. I know a student who's been working on electronic circuits for a quite some time as a hobby before majoring in computer engineering, and although he doesn't have top grades, he has better skills in dealing with actual electronic circuits, more than students with top grades but not actual electronic circuit skills.

 

[dijkarte]

I agree. Students have not time for proper learning because they are left with no enough time. They have to enroll in several courses, finish them in same period, and go on...and they pay for this, not free. Therefore they are left with no option but to get decent marks or just pass...That's what I'm trying to say, we go there to get grades and certificates, then learn later...

 

[homeomorphic]

I don't think it is obsolete. Video technology can substitute some of the functions of the lecture, but there are still a lot of missing functionality, and if you look carefully at *why* people still have 200 person in-class lectures you can see what some of those functions are.

I think the why is just resistance to change.

1) Synchronicity. If you have 200 people going to the same lecture and reading the same page on the same book, then you know who to talk to if you have a problem on that page. Suppose you listen to a lecture on open courseware. You don't understand something. Now what?

Have a FAQ available. Eventually, all conceivable questions will be answered. If that fails, tutoring resources, office hours. Some people would rather show up at office hours, anyway.

2) Feedback. There is a lot of social feedback that happens in a lecture. A professor can look at the class, count the number of students, see how many people are asleep, and then adjust the pace of the course. Also have all of the students in the same room is useful because the students can look at each other, find other students that are in the same class, create social networks, and then complain about the teacher. If you are in a 200 person lecture class, and you are the only one that has difficulty understanding the teacher you are in a completely different situation than if you have 150 people muttering about how incompetent the teacher is.

First of all, videos can incorporate as much feedback as you want from a good sized sample of people studying the material. As far as feedback that is specific to one particular group of people, that can come from homework performance, for example. With videos, the most popular teachers can teach ALL the classes and you can even give the students multiple teachers to choose from, so few will complain about how incompetent the teacher is.

3) Evaluation. If you have everyone in the same room, give the same test, and then look at the scores, it's much easier to figure out what is going on. If you have people taking the same test at different times, then people that take the test later are going to be able to see the earlier answers. If you give different tests, then you are looking at a hellish problem trying to normalize the scores.

What does taking a test have to do with lectures?

4) Group motivation. Just being part of a group is psychologically motivating.

Again, this does little to justify the professor spending so much of his effort to give a lecture that could have been done better by someone else. Just arrange for the students to meet and have study groups or something.

Now all of these things can be worked around (UoP has some interesting solutions to the synchronicity problem), but it's not the case that you can record some videos and declare victory. It's a very tricky problem.

I agree that it's not just a matter of recording videos, but I disagree that it's tricky. Well, in a sense it is tricky because education itself is tricky, period. But it's not tricky to do better than the lecture-based class with 200 students. Or rather, the tricky part is getting people to change their old ways.

 

[twofish-quant]

I think the why is just resistance to change.

That's sort of tauntological. Things don't change because there is resistance to change. The question they becomes why is there resistance to change, and what can be done about it?

Have a FAQ available. Eventually, all conceivable questions will be answered. If that fails, tutoring resources, office hours. Some people would rather show up at office hours, anyway.

But that involves setting up tutoring resources and office hours. One thing about a lecture of 500 people is that I know that if I'm a student in that class that if I show up at the professors office, that he isn't going to be annoyed at me. If I replay a video that was made five years ago, I have no such assurance.

The thing about running a large lecture class is that the instructor of record does more than just lecture. There's the matter of making sure that you have enough tutors, that they are being paid, etc. etc. This *can* be done online, but it's a lot of work. It doesn't happen by magic.

First of all, videos can incorporate as much feedback as you want from a good sized sample of people studying the material. As far as feedback that is specific to one particular group of people, that can come from homework performance, for example. With videos, the most popular teachers can teach ALL the classes and you can even give the students multiple teachers to choose from, so few will complain about how incompetent the teacher is.

1) You don't get instant feedback. If you are give a lecture via video, you can't see how many people are nodding off, how many people have confused looks, and how full the class room is. (You can get around this by having a live studio audience, which is why you have live studio audiences.)

2) Homework performance means setting up homework which gets you back to administrative scale problems. One problem is suppose you get 400 homework assignments. Is that good or bad. You don't know because you don't know the number of people that didn't turn in their homework.

3) Lectures scale. Tutorials don't. You can have Walter Lewin lecture to 10000 people. However, much of learning math and physics involves tutorials, and you can't have more than ten people in a tutorial section before quality suffers.

4) The trouble if you don't synchronize things is that then you have students listening to different instructors, working different problems, and that kills student-student interaction.

Again, none of these are unsolvable problems. However, I claim that as of 2012, that they are *unsolved* problems, although I think they'll rapidly get solved. It's sort of like tablet computing in 2008. At some point, someone somewhere are going to put all of the pieces together.

What does taking a test have to do with lectures?

Without an assessment, you can't turn knowledge into cash, and if you can't turn knowledge into cash, that limits the amount of money that you can spend on the lectures. The lecture is the easy part since that is a fixed cost. The problem are the tutorials and administrative costs. University of Phoenix figured out the solution for business degrees, but no one has tried applying the model to math and science (not even UoP).

Again, this does little to justify the professor spending so much of his effort to give a lecture that could have been done better by someone else. Just arrange for the students to meet and have study groups or something.

The lecture is not that time intensive and it's a fixed cost. It's the "arranging for the students to meet and have study groups" that's the hard part. Again, it's not an unsolvable problem, and MIT has gotten rid of the physics lecture and they now have students meet in a large class and go into small groups in that class.

I agree that it's not just a matter of recording videos, but I disagree that it's tricky. Well, in a sense it is tricky because education itself is tricky, period. But it's not tricky to do better than the lecture-based class with 200 students.

I think it actually is.

Or rather, the tricky part is getting people to change their old ways.

Change to what?

But you have to realize that there are reasons why the old ways exist, and we know that the old ways work, whereas anytime you do something new, you end up with risk. One problem is that if say MIT suddenly changed the way that 18.02 is taught and the new way just doesn't work, then you have a disaster. So what you do is to set up experimental groups and pilot projects, and then as you learn stuff, it goes back into the main sections.

The main problem that I see right now is money. How do you set things up so that either everyone gets paid, or that you have a barter/gift economy in which payment is not necessary? I think it's a solvable problem, but as of 2012, it's an unsolved problem for the undergraduate physics curriculum.

And then there is the motivation problem. Why change? In the 1950's there were *radical* changes in physics, because people believed that without some major changes, everyone in the US would be speaking Russian. There isn't this sort of "light people's pants on fire" motivation that I can see right now.

 

[twofish-quant]

I agree with you that it's wrong to evaluate a person's understanding and skills on a subject according to his grades,

Ummm... I didn't say or imply that it's wrong. I can make the statement that the evaluation system that is used for grading CS courses is not useful in evaluating skills as an applications programmer for the purposes of hiring. That doesn't make the evaluation system right or
wrong.

but what can you do if some teachers, a lot with PhD, think that this is the best strategy to evaluate a student?

1) Play along. Grades are often not useful for evaluating knowledge, but they *are* extremely useful at evaluating some personality skills that companies find useful. If your boss gives you instructions that you think are stupid, you can raise the issue, but in the end if that's what they want, that's what you give them. So part of what grades measure is the ability to follow stupid instructions.

2) Understand why the system is what it is. For example, one problem with the way that most companies evaluate computer programmers is that it's extremely subjective. If I just don't like you, then I can give you a bad evaluation, and there's nothing you can do about it. For some things you want an audit trail. If I give you a standardized test, it may be a *bogus* standardized test, but it's hard to fail someone just because the examiner doesn't like them.

Now in the employment situation, it doesn't matter since "the interviewers just don't like you" is sufficient grounds for you not to get a job as long as the reason they don't like you isn't a prohibited category. Personality is a valid consideration in job interviews.

I have rarely interacted with students who have ambition to learn for the purpose of getting new knowledge and skills, because most of students I interacted with, even those with high grades, pursue good grades and that's their most ambitious goal; how to get an A on that course?

I've found it really easy to deal with this issue. Just create a social situation in which people that care about grades too much don't show up. For example, at UT Austin, you have weekly star parties. No one knows that you've attended, but the people that show up are really interested in astronomy, because why else would they show up? Museums are useful for this. If you go to an art museum, it's a reasonable assumption that most people there are interested in art.

The other thing is that a lot of the problem isn't with the students. It's with the teachers. Students don't just learn the explicit curriculum, but also the hidden curriculum. If you have junior faculty that's obssessed with getting tenure, senior faculty that wants that juicy grant, etc. etc. so that gets taught to the students. It's also the case, that if you don't care about grades, you aren't going to be teaching a course, because the system will have weeded you out.

For that matter one obvious dirty secret that universities found out is that people aren't willing to spend much money if there isn't a payoff. One interesting experiment was Fathom in which some major universities spent tens of millions of dollars on an online platform for online enrichment courses before they figured out that people weren't willing to spend money on enrichment.

They just want to to solve old exams and get a good grade on their new exams. In the first class, the professor put a binomial raised to the third power, and students, although a lot of them have top A grades, couldn't expand the term!

There's a simple solution for this. Have the professor announce on day one that everyone gets an A. You don't have to do any more work, you get an A. Now if anyone wants to stick around and learn math, they can. If not, then happy trails.

I'm willing to bet that if there were 100 students in class on day one, that they'll be at most five on day two.

It's an interesting thought experiment to see what would happen if a professor did that. Everyone here gets an A. By guess is that it will last a week before they find someone else to run the course.

That's one of the reasons I'm opposed to the way university teaches students, because most professors push students to care more about grades rather than real understanding of subjects and developing actual engineering skills.

Unfortunately, I don't see any easy way of coming up with a better system. If people don't compete for grades, they'll compete over something equally bogus. For example, one way schools have tried to make up for being "too academic" is by internship and co-op programs, but then you end up with equally intense competition for getting the right internships on your resume.

The other thing is that companies don't expect fresh students to have real understanding of subjects or engineering skills. What usually happens is that companies usually expect fresh graduates not to have experience. All they want from the school is someone that isn't so incompetent that they are untrainable. If you get an A in object oriented programming, you may know nothing about OOP. *However*, if you get an A in OOP, then it's likely that you can learn it.

I know a student who's been working on electronic circuits for a quite some time as a hobby before majoring in computer engineering, and although he doesn't have top grades, he has better skills in dealing with actual electronic circuits, more than students with top grades but not actual electronic circuit skills.

Which explains why companies aren't obsessed about grades. However, it's really a no win situation. Suppose it became known that people with certain hobbies would find it easier to get jobs. At that point, then everyone that was obsessed about grades suddenly starts being obsessed with having the right hobbies.

I think the problem is a bit deeper. People might disagree, but I really think that the basic problem is that the middle class is disappearing. You either are in the top 1% or the bottom 99%, and the top 1% doesn't have enough spaces for everyone that wants to get in, so there is this mad scramble to get in. It involves getting the right grades, going to the right schools, etc. etc. Curiously I think that academics themselves have a hard time figuring out what to do about this since they are also in this mad scramble to get in.

 

[twofish-quant]

One other interesting sideline is *why* we have lecture classes in physics. Lectures started in the Middle Ages when books were rare, and printing non-existent, so you had someone read from a book, and the students would copy it.

Now fast forward to the 1950's. The US is in a life and death struggle with Russia (or so it seemed). You want to train a ton of physicists and you want to train them *fast*. You have a shortage of teachers and of training materials, so you put everyone in one big room and have a professor talk to them. The methods today are very labor intensive and work when you have few students and a lot of teachers, but they wouldn't have worked in the 1950's, when you had very few teachers and a lot of students.

 

[homeomorphic]

I think the why is just resistance to change.

That's sort of tauntological. Things don't change because there is resistance to change. The question they becomes why is there resistance to change, and what can be done about it?

It's not tautological because what I am referring to is stuff like habits, social conditioning,
not wanting to take risks, rather than having genuine reasons for continuing the old way of doing things.

Have a FAQ available. Eventually, all conceivable questions will be answered. If that fails, tutoring resources, office hours. Some people would rather show up at office hours, anyway.

But that involves setting up tutoring resources and office hours. One thing about a lecture of 500 people is that I know that if I'm a student in that class that if I show up at the professors office, that he isn't going to be annoyed at me. If I replay a video that was made five years ago, I have no such assurance.

Tutoring resources and office hours are already set up, usually. The only thing I'm subtracting is the lecture. Actually, I'm not assured that the professor won't be annoyed with me.

The thing about running a large lecture class is that the instructor of record does more than just lecture. There's the matter of making sure that you have enough tutors, that they are being paid, etc. etc. This *can* be done online, but it's a lot of work. It doesn't happen by magic.

Again, that stuff is already being done. I'm just saying subtract off the lecture. Actually, teachers are already starting to do this in some cases. Their homework is to watch Kahn Academy and class is used for other things. And the results have gotten better.

First of all, videos can incorporate as much feedback as you want from a good sized sample of people studying the material. As far as feedback that is specific to one particular group of people, that can come from homework performance, for example. With videos, the most popular teachers can teach ALL the classes and you can even give the students multiple teachers to choose from, so few will complain about how incompetent the teacher is.

1) You don't get instant feedback. If you are give a lecture via video, you can't see how many people are nodding off, how many people have confused looks, and how full the class room is. (You can get around this by having a live studio audience, which is why you have live studio audiences.)

2) Homework performance means setting up homework which gets you back to administrative scale problems. One problem is suppose you get 400 homework assignments. Is that good or bad. You don't know because you don't know the number of people that didn't turn in their homework.

Again, this is not an argument against merely subtracting the actual lecture.

3) Lectures scale. Tutorials don't. You can have Walter Lewin lecture to 10000 people. However, much of learning math and physics involves tutorials, and you can't have more than ten people in a tutorial section before quality suffers.

That appears to be an argument in favor of my position, since videos also scale.

4) The trouble if you don't synchronize things is that then you have students listening to different instructors, working different problems, and that kills student-student interaction.

Student-student interaction happens during a big lecture? I didn't seem to notice that as being a big part of it. Actually, the place where all the interaction took place when I took freshman physics was in the lab.

Again, none of these are unsolvable problems. However, I claim that as of 2012, that they are *unsolved* problems, although I think they'll rapidly get solved. It's sort of like tablet computing in 2008. At some point, someone somewhere are going to put all of the pieces together.

I think they have been solved, but haven't been implemented on a big scale. I mentioned those teachers using Kahn Academy to replace their lectures.

What does taking a test have to do with lectures?

Without an assessment, you can't turn knowledge into cash, and if you can't turn knowledge into cash, that limits the amount of money that you can spend on the lectures. The lecture is the easy part since that is a fixed cost. The problem are the tutorials and administrative costs. University of Phoenix figured out the solution for business degrees, but no one has tried applying the model to math and science (not even UoP).

Look at the subject GRE tests. Where are the lectures? Test, but no lectures. Why not just subtract the lecture? Not much needs to be changed. Because professors need to be paid, I suppose. But there we see money reasons taking priority of education reasons.

Or rather, the tricky part is getting people to change their old ways.

Change to what?

But you have to realize that there are reasons why the old ways exist, and we know that the old ways work, whereas anytime you do something new, you end up with risk. One problem is that if say MIT suddenly changed the way that 18.02 is taught and the new way just doesn't work, then you have a disaster. So what you do is to set up experimental groups and pilot projects, and then as you learn stuff, it goes back into the main sections.

I don't really see experiments going on, but maybe that's my limited experience. Some of the reasons, as I said, probably are purely sociological, with little or no actual substance to them, and other reasons are just excuses for the purely sociological ones.

The main problem that I see right now is money. How do you set things up so that either everyone gets paid, or that you have a barter/gift economy in which payment is not necessary? I think it's a solvable problem, but as of 2012, it's an unsolved problem for the undergraduate physics curriculum.

And then there is the motivation problem. Why change? In the 1950's there were *radical* changes in physics, because people believed that without some major changes, everyone in the US would be speaking Russian. There isn't this sort of "light people's pants on fire" motivation that I can see right now.

Money is a problem, yes. Which is why I'm glad I never valued it very highly.

 

[SophusLies]

twofish, do you ever argue with yourself? I have to ask. In a thread like this, I'm surprised I haven't seen you quote yourself then bring up a counter point of something you posted several days ago. It seems your main motive in a lot of threads is to talk about the social, economic, or "system" aspect of the given topic.

 

[noobilly]

twofish, for math and science knowledge, do you think it is feasible to have a more exam-based system? Something like say, Calc BC, but on a more advanced and comprehensive scale, so you can show the certificates of exam grades to substitute for a degree.